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Acta Physica Sinica

Testing quantum nonlocality of two-qubit entangled states under decoherence

Qiang Hu, Bai-Yun Zeng, Peng-Yu Gu, Xin-Yan Jia, Dai-He Fan

Published Jan 1, 2022• 4 citations
Publisher

Abstract

The quantum nonlocal correlation of quantum states plays an important role in the quantum information and quantum computing protocols. However, during the transmission of entangled states in the quantum channel, they will inevitably interact with the environment, resulting in the degradation of the coherence and then weakening the quantum nonlocal correlation. Using a high probability quantum nonlocal correlation testing scheme based on Hardy-type paradox, in this paper we investigate the quantum nonlocal correlation testing of two-qubit polarization entangled states when they transmit through amplitude damping channel (ADC), phase damping channel (PDC) and depolarization damping channel (DC). The results show that DC has a great influence on the quantum nonlocal correlation testing, while PDC has little influence on the quantum nonlocal correlation testing of quantum states. Finally, this paper also gives condition for the successful quantum nonlocal correlation testing of ADC under weak measurement and quantum weak measurement reversal operation. The results show that when the intensity of weak measurement increases, the influence of ADC decoherence effect on quantum nonlocal correlation testing can be effectively reduced.

DOI
10.7498/aps.71.20211453

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The quantum nonlocal correlation of quantum states plays an important role in the quantum information and quantum computing protocols. However, during the transmission of entangled states in the quantum channel, they will inevitably interact with the environment, resulting in the degradation of the coherence and then weakening the quantum nonlocal correlation. Using a high probability quantum nonlocal correlation testing scheme based on Hardy-type paradox, in this paper we investigate the quantum nonlocal correlation testing of two-qubit polarization entangled states when they transmit through amplitude damping channel (ADC), phase damping channel (PDC) and depolarization damping channel (DC). The results show that DC has a great influence on the quantum nonlocal correlation testing, while PDC has little influence on the quantum nonlocal correlation testing of quantum states. Finally, this paper also gives condition for the successful quantum nonlocal correlation testing of ADC under weak measurement and quantum weak measurement reversal operation. The results show that when the intensity of weak measurement increases, the influence of ADC decoherence effect on quantum nonlocal correlation testing can be effectively reduced.
Abstract It is known that the inevitable interaction of the entangled qubits with their environments may result in the degradation of quantum correlation. We study the decoherence of two remote qubits under general local single- and two-sided amplitude-damping channel (ADC). By using concurrence, quantum discord and Clauser–Horne–Shimony–Holt (CHSH) inequality, we find that the relation between the residual quantum correlations and the initial ones are different. Recently, Wang et al. [Int. J. Theor. Phys. 54 (2015) 5] showed that there exist a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence, fully entangled fraction and quantum discord, respectively. Here we find that both in single- and two-sided ADC, only the evolution of CHSH inequality with the initial parameter is proportional to that of the initial nonlocality. That means the initial state with maximally nonlocality will retain its role in the evolution. It implies that the evolution of nonlocality may reveal the characteristics of quantum state better. Furthermore, we discuss the evolutions of the three different quantum measurements with the initial parameter under generalized amplitude damping channel (GADC) and find that they are all proportional to that of the initial state.
The observation of the nonlocal properties of multipartite entangled states is of great importance for quantum information protocols. Such properties, however, are fragile and may not be observed in the presence of decoherence exhibited by practical physical systems. In this work we investigate the robustness of the nonlocality of symmetric states experiencing phase and amplitude damping, using suitable Bell inequalities based on an extended version of Hardy's paradox. We derive thresholds for observing nonlocality in terms of experimental noise parameters and demonstrate the importance of the choice of the measurement bases for optimizing the robustness. For WWW states, in the phase damping case, we show that this choice can lead to a trade-off between obtaining a high violation of the nonlocal test and optimal robustness thresholds; we also show that in this setting the nonlocality of WWW states is particularly robust for a large number of qubits. Furthermore, we apply our techniques to the discrimination of symmetric states belonging to different entanglement classes, thus illustrating their usefulness for a wide range of practical quantum information applications.
High-dimensional quantum communication plays an important role in long-distance quantum communication. It is shown that two-qubit quantum entanglement can be protected from amplitude damping decoherence. We study the effect of amplitude damping decoherence on two-qubit high-dimensional quantum entanglement. The negativity for high-dimensional quantum entanglement with or without quantum weak measurement and the reversal in amplitude damping decoherence are presented. We found that nonmaximally entangled state may have better performance than maximally entangled state in amplitude damping decoherence. Moreover, we show that arbitrary high-dimensional quantum entanglement can be protected from amplitude damping decoherence by weak measurement and the reversal. The results of our protocol are in agreement with previous analysis for the case of qubits and qutrits.
In this paper, we investigate the entanglement dynamics of a two-qubit entangled state coupled with its noisy environment, and plan to utilize weak measurement and quantum reversal measurement to study the entanglement dynamics under different decoherence channels in noninertial frames. Through the calculations and analyses, it is shown that the weak measurement can prevent entanglement from coupling to the amplitude damping channel, while the system is under the phase damping and flip channels. This protection protocol cannot prevent entanglement but will accelerate the death of entanglement. In addition, if the system is in the noninertial reference frame, then the effect of weak measurement will be weakened for the amplitude damping channel. Nevertheless, for other decoherence channels, the Unruh effect does not affect the quantum weak measurement, the only exception is that the maximum value of entanglement is reduced to √2/2 of the original value in the inertial frames.
Based on the quantum technique of the weak measurement and quantum measurement reversal (WMR), we propose a scheme to protect entanglement for an entangled two-qubit pure state from four typical quantum noise channels with memory, i.e., the amplitude damping channel, the phase damping channel, the bit flip channel, and the depolarizing channel. For a given initial state | ψ 〉 = a| 00 〉 + d| 11 〉, it is found that the WMR operation indeed helps to protect entanglement from the above four quantum channels with memory, and the protection effect of WMR scheme is better when the coefficient a is small. For the other initial state | ϕ 〉 = b| 01 〉 + c| 10 〉, the effect of the protection scheme is the same regardless of the coefficient b and the WMR operation can protect entanglement in the amplitude damping channel with memory. Moreover, the protection of entanglement in quantum noise channels without memory in contrast to the results of the channels with memory is more effective. For | ψ 〉 or | ϕ 〉, we also find that the memory parameters play a significant role in the suppression of entanglement sudden death and the initial entanglement can be drastically amplified. Another more important result is that the relationship between the concurrence, the memory parameter, the weak measurement strength, and quantum measurement reversal strength is found through calculation and discussion. It provides a strong basis for the system to maintain maximum entanglement in the nosie channel.
Composite quantum systems exhibit non-local correlations. These counter intuitive correlations form a resource for quantum information processing and quantum computation. In our previous work on two qubit maximally entangled mixed states, we observed that entangled states, states that can be used for quantum teleportaion, states that violate Bell-CHSH inequality and states that do not admit local hidden variable description is the hierarchy in terms of the order of nonlocal correlations. In order to establish this hierarchy, in the present work, we investigate the effect of noise on two quibt states that exhibit higher order nonlocal correlations. We find that dilapidation of nonlocal correlations in the presence of noise follow the same hierarchy, that is, higher order nonlocal correlation disappears for small strength of noise, where as lower order nonlocal correlations survive strong noisy environment. We show the results for decoherence due to amplitude damping channel on various quantum states. However, we observe that same hierarchy is followed by states undergoing decoherence due to phase damping as well as depolarizing channels.